Local and global estimation of the contractance rate \(\kappa _\epsilon ()\)  of \(_\)  are detailed respectively in [1]} and [2]}, [3]}.
When \((,)\)  are discrete measures and \(({ij})\)  is a matrix, the latter estimate reads \(\kappa _\epsilon ()\le 1 - \tfrac{2}{1 + \eta }\) , where \(\eta =\exp (-\tfrac{1}{2\epsilon }\max _{i,j,k,l}({j,k} + {i,l} - {j,l} - {i,k}))\) .
Note that \(\eta \)  depends on \(\)  via its support.
